Basic Math Examples

$\frac{100}{2} \cdot 5 + \sqrt{49} - \frac{3}{4} \cdot \frac{16}{27}$

Step 1

Simplify each term.

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Step 1.1

Divide $100$ by $2$ .

$50 \cdot 5 + \sqrt{49} - \frac{3}{4} \cdot \frac{16}{27}$

Step 1.2

Multiply $50$ by $5$ .

$250 + \sqrt{49} - \frac{3}{4} \cdot \frac{16}{27}$

Step 1.3

Rewrite $49$ as $7^{2}$ .

$250 + \sqrt{7^{2}} - \frac{3}{4} \cdot \frac{16}{27}$

Step 1.4

Pull terms out from under the radical, assuming positive real numbers.

$250 + 7 - \frac{3}{4} \cdot \frac{16}{27}$

Step 1.5

Cancel the common factor of $3$ .

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Step 1.5.1

Move the leading negative in $- \frac{3}{4}$ into the numerator.

$250 + 7 + \frac{- 3}{4} \cdot \frac{16}{27}$

Step 1.5.2

Factor $3$ out of $- 3$ .

$250 + 7 + \frac{3 (- 1)}{4} \cdot \frac{16}{27}$

Step 1.5.3

Factor $3$ out of $27$ .

$250 + 7 + \frac{3 \cdot - 1}{4} \cdot \frac{16}{3 \cdot 9}$

Step 1.5.4

Cancel the common factor.

$250 + 7 + \frac{3 \cdot - 1}{4} \cdot \frac{16}{3 \cdot 9}$

Step 1.5.5

Rewrite the expression.

$250 + 7 + \frac{- 1}{4} \cdot \frac{16}{9}$

Step 1.6

Cancel the common factor of $4$ .

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Step 1.6.1

Factor $4$ out of $16$ .

$250 + 7 + \frac{- 1}{4} \cdot \frac{4 (4)}{9}$

Step 1.6.2

Cancel the common factor.

$250 + 7 + \frac{- 1}{4} \cdot \frac{4 \cdot 4}{9}$

Step 1.6.3

Rewrite the expression.

$250 + 7 - 1 \cdot \frac{4}{9}$

Step 1.7

Rewrite $- 1 (\frac{4}{9})$ as $- (\frac{4}{9})$ .

$250 + 7 - \frac{4}{9}$

Step 2

Find the common denominator.

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Step 2.1

Write $250$ as a fraction with denominator $1$ .

$\frac{250}{1} + 7 - \frac{4}{9}$

Step 2.2

Multiply $\frac{250}{1}$ by $\frac{9}{9}$ .

$\frac{250}{1} \cdot \frac{9}{9} + 7 - \frac{4}{9}$

Step 2.3

Multiply $\frac{250}{1}$ by $\frac{9}{9}$ .

$\frac{250 \cdot 9}{9} + 7 - \frac{4}{9}$

Step 2.4

Write $7$ as a fraction with denominator $1$ .

$\frac{250 \cdot 9}{9} + \frac{7}{1} - \frac{4}{9}$

Step 2.5

Multiply $\frac{7}{1}$ by $\frac{9}{9}$ .

$\frac{250 \cdot 9}{9} + \frac{7}{1} \cdot \frac{9}{9} - \frac{4}{9}$

Step 2.6

Multiply $\frac{7}{1}$ by $\frac{9}{9}$ .

$\frac{250 \cdot 9}{9} + \frac{7 \cdot 9}{9} - \frac{4}{9}$

Step 3

Combine the numerators over the common denominator.

$\frac{250 \cdot 9 + 7 \cdot 9 - 4}{9}$

Step 4

Simplify each term.

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Step 4.1

Multiply $250$ by $9$ .

$\frac{2250 + 7 \cdot 9 - 4}{9}$

Step 4.2

Multiply $7$ by $9$ .

$\frac{2250 + 63 - 4}{9}$

Step 5

Simplify by adding and subtracting.

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Step 5.1

Add $2250$ and $63$ .

$\frac{2313 - 4}{9}$

Step 5.2

Subtract $4$ from $2313$ .

$\frac{2309}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\frac{2309}{9}$

Decimal Form:

$256.\overline{5}$

Mixed Number Form:

$256 \frac{5}{9}$